Question 25

[admin]

The calculation is correct.

[admin]

No, you're not missing something, the physics you used is good.

It is true that normally on the MCAT the object immersed is a block. That way, the rule of thumb regarding SG being the fraction of the height submerged is precise. However, given your approximations, you have shown that it is also a reasonable approximation even if the shape is a sphere (the answer being 0.63 g/cc vs 0.67 g/cc with no answer choices even close).

For those who wish to see the proof regarding a block or cube:

Let h = the height of the block
Let x = the height of the block above the surface of the fluid
Let A = the area of the bottom surface of the block

The volume of displaced water is the volume of the object beneath the surface of the water:

V = (h - x) A

As you mentioned, according to Archimedes' principle, the upward buoyant force on the block is the weight of the water displaced:

Fb = W(water) = D(water)g(h - x)A

where D(water) is the density of water. This must balance the weight W of the block:

Fb = W = DgAh

where D is the density of the block. Thus:

D(water)g(h - x)A = DgAh

Cancel "g" and "A" on both sides and rearrange the equation. Now we have the fractional height of the block above the surface of water given by:

x/h = 1 - SG

where SG = D/D(water)


This link below does not have the proof as above but it has an example of its use:

http://webspinners.com/dlblanc/tectonic/floating.php

[dnpgr16513]

Why do you flip 3/4 to 4/3? Please help me!

THANKS

[jellywing_2058]

This is basic math. See the following:

ρball/ρl = 3/4
ρl/pball = 4/3
pl = pball (4/3)
pl = 0.5 g/cm3 x 4/3
pl = 1/2 g/cm3 x 4/3
pl = 2/3 g/cm3
pl = 0.67 g/cm3.

[dnpgr16513]

Ok, great! That's not too bad..

[hua8986059]

I've noticed that the stuff that MCAT likes to stress are the stuff that actually are very medically applicable. I worked at a cardiologist convention where they talked about ideal fluid flow etc... good stuff to learn